%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG391-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:19:55 AM UTC 2026
% Result : Unsatisfiable 2.68s 1.18s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 2
% Syntax : Number of formulae : 6 ( 3 unt; 0 def)
% Number of atoms : 11 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 11 ( 6 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 2 ( 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1407,negated_conjecture,
v_cs____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1410,negated_conjecture,
! [X0] :
( c_Polynomial_Opoly(v_cs____,hAPP(v_x,X0),t_a) != c_Polynomial_Opoly(X0,hAPP(v_x,X0),t_a)
| c_Polynomial_Odegree(X0,t_a) != c_Polynomial_Odegree(v_cs____,t_a)
| X0 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1411,plain,
! [X0] :
( c_Polynomial_Opoly(v_cs____,hAPP(v_x,X0),t_a) != c_Polynomial_Opoly(X0,hAPP(v_x,X0),t_a)
| c_Polynomial_Odegree(X0,t_a) != c_Polynomial_Odegree(v_cs____,t_a)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = X0 ),
inference(reorient_equations,[],[f1410]) ).
fof(f1606,plain,
( c_Polynomial_Odegree(v_cs____,t_a) != c_Polynomial_Odegree(v_cs____,t_a)
| v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(equality_resolution,[],[f1411]) ).
fof(f1607,plain,
v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(trivial_inequality_removal,[],[f1606]) ).
fof(f1608,plain,
$false,
inference(forward_subsumption_resolution,[],[f1607,f1407]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG391-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n010.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 20:15:33 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.68/1.18 % (2267337)Input is clausal, will run a generic CNF schedule.
% 2.68/1.18 % (2267345)lrs+10_1_sil=8000:sp=occurrence:random_seed=2845446118:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.68/1.18 % (2267345)First to succeed.
% 2.68/1.18 % (2267345)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2267337"
% 2.68/1.18 % (2267346)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3635502250:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.68/1.18 % (2267347)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3317061463:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.68/1.18 % (2267344)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3226122486:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.68/1.18 % (2267343)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3258816572:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.68/1.18 % (2267342)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3782173540:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.68/1.18 % (2267348)dis-21_1_sil=8000:lcm=predicate:random_seed=2284691946:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.68/1.18 % (2267346)Also succeeded, but the first one will report.
% 2.68/1.18 % (2267347)Also succeeded, but the first one will report.
% 2.68/1.18 % (2267348)Also succeeded, but the first one will report.
% 2.68/1.18 % (2267345)Refutation found. Thanks to Tanya!
% 2.68/1.18 % SZS status Unsatisfiable for theBenchmark
% 2.68/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.18 % (2267345)------------------------------
% 2.68/1.18 % (2267345)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.18 % (2267345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.18 % (2267345)CaDiCaL version: 2.1.3
% 2.68/1.18 % (2267345)Termination reason: Refutation
% 2.68/1.18 % (2267345)Time elapsed: 0.009 s
% 2.68/1.18 % (2267345)Peak memory usage: 89 MB
% 2.68/1.18 % (2267345)Instructions burned: 25 (million)
% 2.68/1.18 % (2267345)------------------------------
% 2.68/1.18 % (2267345)------------------------------
% 2.68/1.18 % (2267337)Success in time 0.324 s
% 2.68/1.18 % Vampire exiting
%------------------------------------------------------------------------------